Looking at Islamic Patterns I: The Perception of Order

Islamic geometric patterns are complex arrangements of interlocking stars and polygons. They are cultural artefacts rather than stimuli specifically devised for scientific experiments, but they provide a good corpus of test cases to study the human visual system: they have few confounding variables, and contain examples that display convincing combinations of incompatible shapes in configurations that are geometrically impossible. The literature on vision leaves some of their properties unexplained.We define regularities as features of visual data that are processed fluently, and hence depend on properties of the stimulus and the viewer. Useful information is found in non-accidental relationships, and these seem to correspond to regularities for low-level structure that is expected to be seen in the environment. We find that qualitative properties are more salient than metric properties: misalignment between neighbouring stars is more noticeable than imperfect symmetry of individual stars, for example. We develop a model of local symmetry centres, which predicts that stars with odd or even numbers of spikes have different visual properties, and this influences where and how stars should be positioned in a pattern for best effect.